Cambridge & Pearson Edexcel Past Paper Questions
Browse 35,704 questions from Cambridge O-Level & A-Level and Pearson Edexcel IGCSE & IAL exams. Click any question to practice.
The height H, in metres, of mature trees of a certain variety is normally distributed with standard deviation 0.67. In order to test whether the po...
The random variable X has probability density function, f, given by f(x) = { 1/x² a < x < b, 0 otherwise, where a and b are positive constants.
A factory makes loaves of bread in batches. One batch of loaves contains X kilograms of dried yeast and Y kilograms of flour, where X and Y have th...
A random variable X has the distribution Po(2.4).
A random variable X has the distribution N(410, 400).
A biologist wishes to test whether the mean concentration μ, in suitable units, of a certain pollutant in a river is below the permitted level of 0...
The diagram shows the curve with equation y = a sin(bx)+c for 0 ≤ x ≤ 2π, where a, b and c are positive constants. [Figure X.X]
The first term of an arithmetic progression is -20 and the common difference is 5.
The equation of a curve is y = 2x² - 3. Two points A and B with x-coordinates 2 and (2 + h) respectively lie on the curve.
Find the term independent of x in the expansion of each of the following:
The function f is defined by f(x) = (2x+1)/(2x-1) for x < 1/2.
The diagram shows a metal plate OABCDEF consisting of sectors of two circles, each with centre O. The radii of sectors AOB and EOF are r cm and the...
By expressing -2x² +8x+11 in the form -a(x−b)² +c, where a, b and c are positive integers, find the coordinates of the vertex of the graph with equ...
The equation of a circle is x² + y² +px+2y+q = 0, where p and q are constants.
The equation of a curve is y = 1/2 k²x² - 2kx+2 and the equation of a line is y = kx+p, where k and p are constants with 0 < k < 1.
A function f with domain x > 0 is such that f'(x) = 8(2x-3)^(-1/2) - 10x^3. It is given that the curve with equation y = f(x) passes through the po...
The variables x and y satisfy the equation a^(2y) = e^(3x+k), where a and k are constants. The graph of y against x is a straight line.
Solve the inequality |x-7|>4x+3.
The function f is defined by f(x) = tan²(x/2) for 0 < x < π.
The polynomial p(x) is defined by p(x) = ax³ – ax² – 15x + 18, where a is a constant. It is given that (x+2) is a factor of p(x).
It is given that ∫(from a to a³) (10 / (2x+1)) dx = 7, where a is a constant greater than 1.
A curve has parametric equations x = (e^(2t)-2)/(e^(2t)+1), y = e^(3t)+1.
Prove that cos(θ+30°)cos(θ+60°) = (1/4)√3 - (1/2)sin 2θ.
Use logarithms to show that the equation 5⁸ʸ = 6⁷ˣ can be expressed in the form y = kx. Give the value of the constant k correct to 3 significant f...
Let f(x) = 4 sin² 3x. Find the value of f' (π/4).
A curve has equation 6e⁻ˣy² + e²ˣ – 12y + 7 = 0. Find the gradient of the curve at the point (ln 3, 2).
Sketch the graphs of y = 1+e²ˣ and y = |x-4| on the same diagram.
The polynomial p(x) is defined by p(x) = ax³ + bx² - ax + 8, where a and b are constants. It is given that (x + 2) is a factor of p(x), and that th...
The diagram shows the curves with equations y = √5x² +7 and y = 27/(2x+5) for x ≥ 0. The curves meet at the point (2, 3). Region A is bounded by th...
Express 4 sin θ sin(θ+ 60°) in the form a+Rsin(2θ-α), where a and R are positive integers and 0° < α < 90°.
The function f is defined by f(x) = tan²(½x) for 0 ≤ x < π.
It is given that ∫_a^(a³) (10 / (2x+1)) dx = 7, where a is a constant greater than 1.
A curve has parametric equations x = (e^(2t)-2) / (e^(2t)+1), y = e^(3t) + 1.
Prove that cos(θ+30°)cos(θ+60°) = ¼√3 - ½sin 2θ.
The polynomial 4x³ + ax² +5x+b, where a and b are constants, is denoted by p(x). It is given that (2x+1) is a factor of p(x). When p(x) is divided ...
Find the exact value of ∫ x² ln 3x dx. Give your answer in the form a lnb+c, where a and c are rational and b is an integer.
The equation of a curve is ln(x+y) = 3x²y. Find the gradient of the curve at the point (1,0).
Show that sec⁴θ-tan⁴θ = 1+2tan²θ.
Hence or otherwise solve the equation sec⁴2α-tan⁴ 2α = 2 tan² 2α sec² 2α for 0° < α < 180°.
By sketching a suitable pair of graphs, show that the equation 2+e-0.2x = ln(1+x) has only one root.
Show by calculation that this root lies between 7 and 9.
Use the iterative formula x_n+1 = exp(2+e-0.2x_n) - 1 to determine the root correct to 2 decimal places. Give the result of each iteration to 4 dec...
The diagram shows the curve y = sin2x(1+sin2x), for 0 ≤ x ≤ ¾π, and its minimum point M. The shaded region bounded by the curve that lies above the...
Let f(x) = (5x²+8x+5) / ((1+2x)(2+x²))
Given that z = 1+yi and that y is a real number, express 1/z in the form a+bi, where a and b are functions of y.
Show that (a-½)²+b² = ¼, where a and b are the functions of y found in part (a).
On a single Argand diagram, sketch the loci given by the equations Re(z) = 1 and |z - ½| = ½, where z is a complex number.
The complex number z is such that Re(z) = 1. Use your answer to part (b) to give a geometrical description of the locus of 1/z.
The position vector of point A relative to the origin O is OA = 8i−5j+6k. The line l passes through A and is parallel to the vector 2i+j+4k.
A large cylindrical tank is used to store water. The base of the tank is a circle of radius 4 metres. At time t minutes, the depth of the water in ...